A note on drastic product logic

The drastic product $*_D$ is known to be the smallest $t$-norm, since $x *_D y = 0$ whenever $x, y < 1$. This $t$-norm is not left-continuous, and hence it does not admit a residuum. So, there are no drastic product $t$-norm based many-valued logics, in the sense of [EG01]. However, if we renounce standard completeness, we can study the logic whose semantics is provided by those MTL chains whose monoidal operation is the drastic product. This logic is called ${\rm S}_{3}{\rm MTL}$ in [NOG06]. In this note we justify the study of this logic, which we rechristen DP (for drastic product), by means of some interesting properties relating DP and its algebraic semantics to a weakened law of excluded middle, to the $\Delta$ projection operator and to discriminator varieties. We shall show that the category of finite DP-algebras is dually equivalent to a category whose objects are multisets of finite chains. This duality allows us to classify all axiomatic extensions of DP, and to compute the free finitely generated DP-algebras.Comment: 11 pages, 3 figure

The Character of Z-pole Data Constraints on Standard Model Parameters

Despite the impressive precision of the Z-pole measurements made at LEP and SLC, the allowed region for the principle Standard Model parameters responsible for radiative corrections (the mass of the Higgs, the mass of the top and alpha(Mz)) is still large enough to encompass significant non-linearities. The nature of the experimental constraints therefore depends in an interesting way on the "accidental" relationships among the various measurements. In particular, the fact that the Z-pole measurements favor values of the Higgs mass excluded by direct searches leads us to examine the effects of external Higgsstrahlung, a process ignored by the usual precision electroweak calculations.Comment: 9 pages, 6 figures, REVTeX format; added reference in section IV; added paragraph on widths and a few cosmetic changes to correspond to published versio

Stable non-standard imprecise probabilities

Stability arises as the consistency criterion in a betting interpretation for hyperreal imprecise previsions, that is imprecise previsions (and probabilities) which may take infinitesimal values. The purpose of this work is to extend the notion of stable coherence introduced in [8] to conditional hyperreal imprecise probabilities. Our investigation extends the de Finetti-Walley operational characterisation of (imprecise) prevision to conditioning on events which are considered "practically impossible" but not "logically impossible"

Bayesian isotonic logistic regression via constrained splines: an application to estimating the serve advantage in professional tennis

In professional tennis, it is often acknowledged that the server has an initial advantage. Indeed, the majority of points are won by the server, making the serve one of the most important elements in this sport. In this paper, we focus on the role of the serve advantage in winning a point as a function of the rally length. We propose a Bayesian isotonic logistic regression model for the probability of winning a point on serve. In particular, we decompose the logit of the probability of winning via a linear combination of B-splines basis functions, with athlete-specific basis function coefficients. Further, we ensure the serve advantage decreases with rally length by imposing constraints on the spline coefficients. We also consider the rally ability of each player, and study how the different types of court may impact on the player’s rally ability. We apply our methodology to a Grand Slam singles matches dataset

The changing Chinese community in London: new migration, new needs.

London’s Chinese population in London is one of the most rapidly growing of any national group and is becoming increasingly diverse as new forms of migration develop and people arrive from regions of China which have previously seen little emigration. These developments are a product of political and economic changes in both China and in Britain. The ending of restrictions on travel within China and its growing participation in the global economy have opened up new opportunities for internal and international migration. These new migrants include the most privileged - students, the highly skilled with established jobs in London - as well as those for whom China’s transformation to a market economy has meant dispossession and loss of livelihood. Many have been forced to emigrate for survival, often leaving family in China. Britain, with other European countries, has become increasingly dependent on migrant labour but immigration policies are increasingly selective, welcoming those with recognised skills while restricting entry to those deemed unskilled. Many of the new thus migrants find themselves forced to rely on ‘agents’ to enter the country and their insecure status means they have limited rights once they have arrived and are vulnerable to exploitation. The deaths of 20 Chinese cockle pickers in Morecambe Bay in 2004 drew attention to the ‘hidden’ population of new Chinese migrants. Many new migrants prosper and are able to take advantage of the opportunities which migration brings, but others, especially those with insecure legal and economic status, may struggle, often over a protracted period, to gain a foothold in British society. They may speak little English, have limited knowledge of British society and are poorly prepared to settle and find adequate work. They need support in order to access services, but many have little information about how to go about this and limited social networks to help them. Most of the established Chinese population in London migrated to Britain from Hong Kong and speak Cantonese, unlike the predominantly Mandarin-speaking new migrants. They have established a range of community, business and cultural organisations but these mainly cater for earlier generations. Some have struggled to respond to the new needs which these new migrants bring, but they often lack the necessary knowledge, language and resources. This report is based on research which focused on the experiences of this new population and ways in which service providers could support them in order to promote their inclusion. Although we focus on new migrants, we acknowledge that there is widespread poverty, exclusion and isolation among older generations of Chinese people, particularly as they reach retirement age. The research included all those identifying their ethnic origin as Chinese, including people from Hong Kong, Taiwan, Thailand and Vietnam. The majority of participants, however, came from mainland China. The study was based in London which has the largest and most diverse Chinese population in Britain and many Chinese organisations. We hope, however, that its findings and recommendations will also be relevant to the Chinese population across Britain. The research was carried out by researchers based at Middlesex University and working with Chinese community organisations in London. We are grateful to the Big Lottery Fund for their financial support and to the School of Health and Social Science at Middlesex University whose contribution ensured that the project was completed. We also wish to thank the informants from Chinese community organisations and the individuals interviewed for the research who have contributed generously with their time and ideas

The Raman coupling function in amorphous silica and the nature of the long wavelength excitations in disordered systems

New Raman and incoherent neutron scattering data at various temperatures and molecular dynamic simulations in amorphous silica, are compared to obtain the Raman coupling coefficient $C(\omega)$ and, in particular, its low frequency limit. This study indicates that in the $\omega \to 0$ limit $C(\omega)$ extrapolates to a non vanishing value, giving important indications on the characteristics of the vibrational modes in disordered materials; in particular our results indicate that even in the limit of very long wavelength the local disorder implies non-regular local atomic displacements.Comment: Revtex, 4 ps figure